The neutral lithium atom has three electrons. The spectroscopic notation for it is LiI. The ground state electron configuration of LiI is (1s)2(2s)1. LiI has a series of excited states in which the 2s electron has been raised to some (nl) level. Singly ionized lithium, denoted by LiII, has two electrons. It is made by removing the 2s electron from the atom. The energy levels of the LiI states relative to the energy of LiII are:
The negative sign indicates that energy is required to remove an electron from LiI to form LiII. For example, 5.390 eV is required to remove the 2s electron from LiI When LiI is in one of its excited states, it takes less energy to remove the electron.
-5.390 -3.542 eV 2s, 2p -2.016 -1.555 -1.511 3s, 3p, 3d -1.048 -0.867 -0.852 -0.848 4s, 4p, 4d, 4f
a) What is the ionization energy of LiI?
The ionization energy of LiI is eV.
b) How many of the energies listed above correspond to the (1s)2(np)1 configuration?
energies.
The energy levels for given n depend on l because of different shielding of the nucleus by the two inner electrons. The energies can be given by the expression
.
c) Find Zeff, the effective nuclear charge, for the n = 3 levels: 3s, 3p, and 3d.
Zeff for 3s =
Zeff for 3p =
Zeff for 3d =
d) For which level, 3s, 3p, or 3d, is the shielding of the nucleus greatest?
Level is
To do rest of the problem it is necessary to draw an energy level diagram for these levels using separate columns for s, p, d, and f states. Here is an old lecture slide that illustrates (for sodium) the kind of diagram you should draw.
e) Let a large number of Li atoms be initially excited to the 4p state, and assume they cascade to the ground state following the dipole transition selection rule: Dl = ±1. How many different requencies of light are emitted in the process? It will be useful to indicate the allowed transitions on your diagram for the previous question. (Each possible (ni, li) -> (nf, lf ) counts as one transition.)
different frequencies
f) Find the energies of the most energetic and the least energetic transitions found in the cascade from the 4p level.
Most energetic: eV
Least energetic: eV
Some of the allowed transitions found above would also be seen in the absorption spectrum of LiI.
g) Find the energies of the most energetic and the least energetic transitions that would also be seen in the absorption spectrum, assuming that atoms excited by absorbing a photon stay in the excited state such a short time that the probability of absorbing another photon while in the excited state is negligibly small.
Most energetic: eV
Least energetic: eV
